5p^2=-23p-12

Solution for 5p^2=-23p-12 equation:

Simplifying
5p2 = -23p + -12

Reorder the terms:
5p2 = -12 + -23p

Solving
5p2 = -12 + -23p

Solving for variable 'p'.

Reorder the terms:
12 + 23p + 5p2 = -12 + -23p + 12 + 23p

Reorder the terms:
12 + 23p + 5p2 = -12 + 12 + -23p + 23p

Combine like terms: -12 + 12 = 0
12 + 23p + 5p2 = 0 + -23p + 23p
12 + 23p + 5p2 = -23p + 23p

Combine like terms: -23p + 23p = 0
12 + 23p + 5p2 = 0

Factor a trinomial.
(4 + p)(3 + 5p) = 0

Subproblem 1
Set the factor '(4 + p)' equal to zero and attempt to solve:

Simplifying
4 + p = 0

Solving
4 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + p = 0 + -4
p = 0 + -4

Combine like terms: 0 + -4 = -4
p = -4

Simplifying
p = -4
Subproblem 2
Set the factor '(3 + 5p)' equal to zero and attempt to solve:

Simplifying
3 + 5p = 0

Solving
3 + 5p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 5p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5p = 0 + -3
5p = 0 + -3

Combine like terms: 0 + -3 = -3
5p = -3

Divide each side by '5'.
p = -0.6

Simplifying
p = -0.6
Solution
p = {-4, -0.6}